Simplify the following expression: $ n = \dfrac{1}{5} - \dfrac{k + 4}{7k - 8} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7k - 8}{7k - 8}$ $ \dfrac{1}{5} \times \dfrac{7k - 8}{7k - 8} = \dfrac{7k - 8}{35k - 40} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{k + 4}{7k - 8} \times \dfrac{5}{5} = \dfrac{5k + 20}{35k - 40} $ Therefore $ n = \dfrac{7k - 8}{35k - 40} - \dfrac{5k + 20}{35k - 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{7k - 8 - (5k + 20) }{35k - 40} $ Distribute the negative sign: $n = \dfrac{7k - 8 - 5k - 20}{35k - 40}$ $n = \dfrac{2k - 28}{35k - 40}$